一类二阶超定双曲型复方程组的Riemann—Hilbert边值问题

考察了多双曲复数空间中，一类二阶超定双曲型复方程组（δ^2ω/δziδzk）=（fik）,i,k=1,2,z∈D在一般柱型域上的Riemann—Hilbert边值问题。通过引入新的函数把问题转化为先求两个一阶超定双曲型复方程组，即广义多双曲正则函数在一般柱型域上的Riemann—Hilbert边值问题，由已有结果得到它们各自的解，然后再把原问题化为一个一阶超定双曲型复方程组的Riemann—Hilbert边值问题，在一般柱型域上通过函数论的方法获得了其可解条件，解的积分表示以及解的唯一性。

Riemann-Hilbert Boundary Value Problem in a Class of Overdetermined Hyperbolic Equations of Second Order

In this paper, we study the Riemann-Hilbert boundary value problems in the general bicylinder in a class of overdetermined hyperbolic equations of second order （δ^2ω/δziδzk）=（fik）,i,k=1,2,z∈D in the several hyperbolic complex space. Firstly, with new functions we translate the Riemann-Hilbert boundary value problems to two Riemann-Hilbert boundary value problems in overdetermined hyperbolic equations of first order, or the generalized hyperbolic regular functions in the general bicylinder, and obtain the representations of the solutions, because the problems have been solvedly. Secondly, we must deal with the Riemann-Hilbert boundary value problems in a class of overdetermined hyperbolic equations of first order that being equivalent to the Riemann-Hilbert boundary value problems in the general bicylinder in that class of overdetermined hyperbolic equations of second order to discuss the question. In the general bicylinder, with theory of functions method, we get conditions for its solvability, prove its solvability of the problem, and give the integral representations of the solution and its uniqueness.